The culture that I live in here in the Czech Republic would paint your statement as pretty false. The police here are extremely laid-back and it's pretty easy to get away with petty thievery, yet crime is exceptionally low because people are not desperate enough to risk even the low chance of getting in trouble. You only take chances when you have nothing to lose and you only have nothing to lose when you have been completely excluded from society.
In addition to avoiding the risk, it just feels good to play by the rules if you think the system is reasonably just. I suspect a large fraction of people prefer to be honest and pay for the products and services they want.